The DT, which is originally the frame work of Darboux [1]}, is a powerful method for constructing solutions for integrable systems. In view to obtain rogue wave solutions for the nonlinear wave equations, the original DT is not applicable directly. So Matveev [2]} introduced the so-called generalized DT and the positon solutions were calculated for the KdV equation [2]}. Then, Guo et al. [4]} re-examined Matveev's generalized DT and proposed a new approach to derive the generalized DT for the KdV and the NLS equations. The Guo et al [4]}'s approach has been used in this work to derive higher-order rogue wave for the Manakov system (REF ) and (REF ).
